The languages of spacetime
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFMG |
Texto Completo: | http://hdl.handle.net/1843/58363 |
Resumo: | The theory of general relativity emerges in 1915, and its mathematical stage is a four-dimensional Lorentzian manifold. Our goal will be to explore different languages and formulations of the theory, with different quantities playing the role of dynamical variables. We will start with the original formulation of the theory developed by Einstein, and then pass to the Lagrangian formulation, first developed by Hilbert. Then we will develop two Hamiltonian formulations of gravity, based on a (3+1) foliation of spacetime. The first will be done with the three-dimensional spatial metric as dynamical variable. Such a formalism is known as the ADM formalism of general relativity and allows for the construction of a Hamiltonian for the theory in terms of constraints and Lagrange multipliers. Finally, we will analyze the Hamiltonian formalism based on the Holst action, in terms of Ashtekar variables. This formulation provides a possible path for the canonical quantization of the gravitational field, in the approach known as loop quantum gravity. |
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Nelson de Oliveira Yokomizohttp://lattes.cnpq.br/8910446770279026Mário Sérgio de Carvalho MazzoniGláuber Carvalho Dorschhttp://lattes.cnpq.br/5464626057578263Felipe Brandão Guisoli2023-08-31T16:28:18Z2023-08-31T16:28:18Z2022-12-20http://hdl.handle.net/1843/58363The theory of general relativity emerges in 1915, and its mathematical stage is a four-dimensional Lorentzian manifold. Our goal will be to explore different languages and formulations of the theory, with different quantities playing the role of dynamical variables. We will start with the original formulation of the theory developed by Einstein, and then pass to the Lagrangian formulation, first developed by Hilbert. Then we will develop two Hamiltonian formulations of gravity, based on a (3+1) foliation of spacetime. The first will be done with the three-dimensional spatial metric as dynamical variable. Such a formalism is known as the ADM formalism of general relativity and allows for the construction of a Hamiltonian for the theory in terms of constraints and Lagrange multipliers. Finally, we will analyze the Hamiltonian formalism based on the Holst action, in terms of Ashtekar variables. This formulation provides a possible path for the canonical quantization of the gravitational field, in the approach known as loop quantum gravity.A teoria da relatividade geral surge em 1915, e seu palco matemático é uma variedade quadridimensional Lorentziana. Nosso objetivo será explorar diferentes linguagens e formulações da teoria, com diferentes parâmetros atuando como variáveis dinâmicas. Iniciaremos com a formulação original desenvolvida por Einstein e passaremos então para a formulação lagrangeana da teoria, desenvolvida primeiramente por Hilbert. Desenvolveremos então duas formulações hamiltonianas da gravitação, baseadas em uma folheação (3+1) do espaço-tempo. A primeira será feita com o uso da métrica tridimensional como variável dinâmica. Tal formalismo é conhecido como formalismo ADM da relatividade geral e possibilita a construção de uma Hamiltoniana para a teoria em termos de vínculos e multiplicadores de Lagrange. Por fim, analisaremos a formulação hamiltoniana baseada na ação de Holst, em termos das variáveis de Ashtekar. Tal formulação é um dos caminhos possíveis para a quantização do campo gravitacional, na abordagem conhecida como gravitação de laços.CNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em FísicaUFMGBrasilICX - DEPARTAMENTO DE FÍSICAhttp://creativecommons.org/licenses/by-nc-nd/3.0/pt/info:eu-repo/semantics/openAccessRelatividade geralGravitaçãoRelatividade geralGravitaçãoFormalismo hamiltonianoVariáveis de AshtekarGravitação quântica de laçosThe languages of spacetimeAs linguagens do espaço-tempoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALThe Languages of Spacetime.pdfThe Languages of Spacetime.pdfAtualização 29/08/2023application/pdf20817975https://repositorio.ufmg.br/bitstream/1843/58363/3/The%20Languages%20of%20Spacetime.pdfdb714601e22dab7bc9a1a2690864eb63MD53CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufmg.br/bitstream/1843/58363/4/license_rdfcfd6801dba008cb6adbd9838b81582abMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/58363/5/license.txtcda590c95a0b51b4d15f60c9642ca272MD551843/583632023-08-31 13:28:18.947oai:repositorio.ufmg.br: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ório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2023-08-31T16:28:18Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false |
dc.title.pt_BR.fl_str_mv |
The languages of spacetime |
dc.title.alternative.pt_BR.fl_str_mv |
As linguagens do espaço-tempo |
title |
The languages of spacetime |
spellingShingle |
The languages of spacetime Felipe Brandão Guisoli Relatividade geral Gravitação Formalismo hamiltoniano Variáveis de Ashtekar Gravitação quântica de laços Relatividade geral Gravitação |
title_short |
The languages of spacetime |
title_full |
The languages of spacetime |
title_fullStr |
The languages of spacetime |
title_full_unstemmed |
The languages of spacetime |
title_sort |
The languages of spacetime |
author |
Felipe Brandão Guisoli |
author_facet |
Felipe Brandão Guisoli |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Nelson de Oliveira Yokomizo |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8910446770279026 |
dc.contributor.referee1.fl_str_mv |
Mário Sérgio de Carvalho Mazzoni |
dc.contributor.referee2.fl_str_mv |
Gláuber Carvalho Dorsch |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/5464626057578263 |
dc.contributor.author.fl_str_mv |
Felipe Brandão Guisoli |
contributor_str_mv |
Nelson de Oliveira Yokomizo Mário Sérgio de Carvalho Mazzoni Gláuber Carvalho Dorsch |
dc.subject.por.fl_str_mv |
Relatividade geral Gravitação Formalismo hamiltoniano Variáveis de Ashtekar Gravitação quântica de laços |
topic |
Relatividade geral Gravitação Formalismo hamiltoniano Variáveis de Ashtekar Gravitação quântica de laços Relatividade geral Gravitação |
dc.subject.other.pt_BR.fl_str_mv |
Relatividade geral Gravitação |
description |
The theory of general relativity emerges in 1915, and its mathematical stage is a four-dimensional Lorentzian manifold. Our goal will be to explore different languages and formulations of the theory, with different quantities playing the role of dynamical variables. We will start with the original formulation of the theory developed by Einstein, and then pass to the Lagrangian formulation, first developed by Hilbert. Then we will develop two Hamiltonian formulations of gravity, based on a (3+1) foliation of spacetime. The first will be done with the three-dimensional spatial metric as dynamical variable. Such a formalism is known as the ADM formalism of general relativity and allows for the construction of a Hamiltonian for the theory in terms of constraints and Lagrange multipliers. Finally, we will analyze the Hamiltonian formalism based on the Holst action, in terms of Ashtekar variables. This formulation provides a possible path for the canonical quantization of the gravitational field, in the approach known as loop quantum gravity. |
publishDate |
2022 |
dc.date.issued.fl_str_mv |
2022-12-20 |
dc.date.accessioned.fl_str_mv |
2023-08-31T16:28:18Z |
dc.date.available.fl_str_mv |
2023-08-31T16:28:18Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
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masterThesis |
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publishedVersion |
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http://hdl.handle.net/1843/58363 |
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http://hdl.handle.net/1843/58363 |
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eng |
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eng |
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http://creativecommons.org/licenses/by-nc-nd/3.0/pt/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/3.0/pt/ |
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openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Física |
dc.publisher.initials.fl_str_mv |
UFMG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
ICX - DEPARTAMENTO DE FÍSICA |
publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
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